Is there a way to export each render layer seperate but as animation?
Yes this is possible, for this you will need to use the compositor.

Activate use nodes and delete the composite output node.
You will be left with a Render Layers input node.
Create a copy of this node for each render layer you wish to create output, and select a separate render layer for each node.
Connect a File Output node to each Render Layers node using the yellow image connection dots.
Create a separate output path for each file output node.